2.15
Orifices
FE
W. H. HOWE (1969) B. G. LIPTÁK (1995), REVIEWED BY S. RUDBÄCH J. B. ARANT (1982, 2003)
In Quick Change Fitting FO
FE
Flange Taps
FE
Fixed Restriction
FT
Vena Contracta Taps or Radius Taps
Integral Orifice Transmitter
Flow Flow She Sheet S ymbo ymbol l
Design Pressure
For plates, limited by readout device only; integral orifice transmitter to 1500 PSIG (10.3 MPa)
Design Temperatur Temperaturee
This is a function of associated readout system, only when the differential-pressure unit must operate at the elevated temperature. For integral orifice transmitter, the standard range is −20 to 250°F ( −29 to 121°C).
Sizes
Maximum size is pipe size
Fluids
Liquids, vapors, and gases
Flow Range
From a few cubic centimeters per minute using integral orifice transmitters to any maximum flow, limited only by pipe size
Materials of Construction
There is no limitation on plate materials. Integral orifice transmitter wetted parts can ® ® be obtained in steel, stainless steel, Monel , nickel, and Hastelloy .
Inaccuracy
The orifice plate; if the bore diameter is correctly calculated, prepared, and installed, the orifice can be accurate to ±0.25 to ±0.5% of actual flow. When a properly calibrated conventional d/p cell is used to detect the orifice differential, it will add ±0.1 to ±0.3% of full-scale error. The error contribution of properly calibrated “smart” d/p cells is only 0.1% of actual span.
Smart d/p Cells
Inaccuracy of ±0.1%, rangeability of 40:1, built-in PID algorithm
Rangeability
If one defines rangeability as the flow range within which the combined flow measurement error does not exceed ±1% of actual flow, then the rangeability of conventional orifice installations is about 3:1 maximum. When using intelligent transmitters with automatic switching capability between the “high” and the “low” span, the rangeability can approach 10:1.
Cost
A plate only is $100 to $300, depending on size and materials. For steel orifice flanges from 2 to 12 in. (50 to 300 mm), the cost ranges from $250 to $1200. For flanged meter runs in the same size range, the cost ranges from $500 to $3500. The cost of electronic or pneumatic integral orifice transmitters is between $1500 and $2500. The cost of d/p transmitters ranges from $1000 to $2500, depending on type and “intelligence.”
Partial List of Suppliers
ABB Process Automation (www.abb.com/processautomation (www.abb.com/processautomation)) (incl. integral orifices) Daniel Measurement and Control (www.danielind.com (www.danielind.com)) (orifice plates and plate changers) The Foxboro Co. (www.foxboro.com www.foxboro.com)) (incl. integral orifices) Honeywell Industrial Control (www.honeywell.com/acs/cp (www.honeywell.com/acs/cp)) Meriam Instrument (www.meriam.com (www.meriam.com)) (orifice plates) Rosemount Inc. (www.rosemount.com (www.rosemount.com)) Tri-Flow Inc. (www.triflow.com (www.triflow.com))
259 © 2003 by Béla Lipták
260
Flow Measurement
In addition, orifice plates, flanges and accessories can be obtained from most major instrument manufacturers.
data, more accurate and versatile test and calibrating equipment, better differential-pressure sensors, and many others.
Theory of Head Meters HEAD-TYPE FLOWMETERS Head-type flowmeters compose a class of devices for fluid flow measurement including ori fice plates, venturi tubes, weirs, flumes, and many others. They change the velocity or direction of the flow, creating a measurable differential pressure or “pressure head” in the fluid. Head metering is one of the most ancient of flow detection techniques. There is evidence that the Egyptians used weirs for measurement of irrigation water in the days of the Pharaohs and that the Romans used ori fices to meter water to households in Caesar’s time. In the 18th century, Bernoulli established basic relationship between pressure head and velocity head, and Venturi published on the flowtube bearing his name. However, it was not until 1887 that Clemens Herschel developed the commercial venturi tube. Work on the conventional orifice plate for gas flow measurement was commenced by Weymouth in the United States in 1903. Recent developments include improved primary elements, re finement of
Head-type flow measurement derives from Bernoulli ’s theorem, which states that, in a flowing stream, the sum of the pressure head, the velocity head, and the elevation head at one point is equal to their sum at another point in the direction of flow plus the loss due to friction between the two points. Velocity head is de fined as the vertical distance through which a liquid would fall to attain a given velocity. Pressure head is the vertical distance that a column of the flowing liquid would rise in an open-ended tube as a result of the static pressure. This principle is applied to flow measurement by altering the velocity of the flowing stream in a predetermined manner, usually by a change in the cross-sectional area of the stream. Typically, the velocity at the throat of an ori fice is increased relative to the velocity in the pipe. There is a corresponding increase in velocity head. Neglecting friction and change of elevation head, there is an equal decrease in pressure head (Figure 2.15a). This difference between the pressure in the pipe just upstream of the restriction and the pressure at the throat is measured. Velocity is determined from the ratio of
Static Pressure
∆PPT
∆PRT = ∆PVC
∆PCT
∆PFT
(0.35−0.85)D
Unstable Region, No Pressure Tap Can Be Located Here
Pressure at Vena Contracta (PVC) Minimum Diameter
Flow
2.5D
D
1" 1"
8D
D/2 Corner Taps (CT), D < 2"
Flange Taps (FT), D > 2" Radius Taps (RT), D > 6" Pipe Taps (PT)
D
Orifice
FIG. 2.15a Pressure profile through an orifice plate and the different methods of detecting the pressure drop.
© 2003 by Béla Lipták
Flow
2.15 Orifices
the cross-sectional areas of pipe and flow nozzle, and the difference of velocity heads given by differential-pressure measurements. Flow rate derives from velocity and area. The basic equations are as follows: V
=
k
Q = kA
W
=
h
ρ h
ρ
kA hρ
2.15(1)
2.15(2)
2.15(3)
where V = velocity Q = volume flow rate W = mass flow rate A = cross-sectional area of the pipe h = differential pressure between points of measurement ρ = the density of the flowing fluid k = a constant that includes ratio of cross-sectional area of pipe to cross-sectional area of nozzle or other restriction, units of measurement, correction factors, and so on, depending on the speci fic type of head meter For a more complete derivation of the basic flow equations, based on considerations of energy balance and hydrodynamic properties, consult References 1, 2, and 3.
Head Meter Characteristics Two fundamental characteristics of head-type flow measurements are apparent from the basic equations. First is the squar e root relationship between flow rate and differential pressure. Second, the density of the flowing fluid must be taken into account both for volume and for mass flow measurements. The Square Root Relationship This relationship has two important consequences. Both are primarily concerned with readout. The primary sensor (ori fice, venturi tube, or other device) develops a head or differential pressure. A simple linear readout of this differential pressure expands the high end of the scale and compresses the low end in terms of flow. Fifty percent of full flow rate produces 25% of full differential pressure. At this point, a flow change of 1% of full flow results in a differential pressure change of 1% of full differential. At 10% flow, the total differential pressure is only 1%, and a change of 1% of full scale flow (10% relative change) results in only 0.2% full scale change in differential pressure. Both accuracy and readability suffer. Readability can be improved by a transducer that extracts the square root of the differential pressure to give a signal linear with flow rate. However, errors in the more complex square root transducer tend to decrease overall accuracy.
© 2003 by Béla Lipták
261
For a large proportion of industrial processes, which seldom operate below 30% capacity, a device with pointer or pen motion that is linear with differential pressure is generally adequate. Readout directly in flow can be provided by a square root scale. Where maximum accuracy is important, it is generally recommended that the maximum-to-minimum flow ratio shall not exceed 3:1, or at the most 3.5:1, for any single head-type flowmeter. The high repeatability of modern differential-pressure transducers permits a considerably wider range for flow control where constancy and repeatability of low rate are the primary concern. However, where flow variations approach 10:1, the use of two primary flow units of different capacities, two differential-pressure sensors with different ranges, or both is generally recommended. It should be emphasized that the primary head meter devices produce a differential pressure that corresponds accurately to flow over a wide range. Dif ficulty arises in the accurate measurement of the corresponding extremely wide range of differential pressure; for example, a 20:1 flow variation results in a 400:1 variation in differential pressure. The second problem with the square root relationship is that some computations require linear input signals. This is the case when flow rates are integrated or when two or more flow rates are added or subtracted. This is not necessarily true for multiplication and division; speci fically, flow ratio measurement and control do not require linear input signals. A given flow ratio will develop a corresponding differential pressure ratio over the full range of the measured flows. Density of the Flowing Fluid Fluid density is involved in the determination of either mass flow rate or volume flow rate. In other words, head-type meters do not read out directly in either mass or volume flow (weirs and flumes are an exception, as discussed in Section 2.31). The fact that density appears as a square root gives head-type metering an actual advantage, particularly in applications where measurement of mass flow is required. Due to this square root relationship, any error that may exist in the value of the density used to compute mass flow is substantially reduced; a 1% error in the value of the fluid density results in a 0.5% error in calculated mass flow. This is particularly important in gas flow measurement, where the density may vary over a considerable range and where operating density is not easily determined with high accuracy.
β (Beta) Ratio Most head meters depend on a restriction in β the flow path to produce a change in velocity. For the usual circular pipe and circular restriction, the β ratio is the ratio between the diameter of the restriction and the inside diameter of the pipe. The ratio between the velocity in the pipe and the velocity at the restriction is equal to the ratio of areas 2 or β . For noncircular configurations, β is defined as the square root of the ratio of area of the restriction to area of the pipe or conduit.
262
Flow Measurement
Reynolds Number
Coefficient of Discharge Concentric Square Edged Orifice
The basic equations of flow assume that the velocity of flow is uniform across a given cross section. In practice, flow velocity at any cross section approaches zero in the boundary layer adjacent to the pipe wall and varies across the diameter. This flow velocity profile has a signi ficant effect on the relationship between flow velocity and pressure difference developed in a head meter. In 1883, Sir Osborne Reynolds, an English scientist, presented a paper before the Royal Society proposing a single, dimensionless ratio (now known as Reynolds number) as a criterion to describe this phenomenon. This number, Re, is expressed as
Eccentric Orifice
=
VDρ
µ
2.15(4)
where V = velocity D = diameter ρ = density µ = absolute viscosity Reynolds number expresses the ratio of inertial forces to viscous forces. At a very low Reynolds number, viscous forces predominate, and inertial forces have little effect. Pressure difference approaches direct proportionality to average flow velocity and to viscosity. At high Reynolds numbers, inertial forces predominate, and viscous drag effects become negligible. At low Reynolds numbers, flow is laminar and may be regarded as a group of concentric shells; each shell reacts in a viscous shear manner on adjacent shells, and the velocity pro file across a diameter is substantially parabolic. At high Reynolds numbers, flow is turbulent, with eddies forming between the boundary layer and the body of the flowing fluid and propagating through the stream pattern. A very complex, random pattern of velocities develops in all directions. This turbulent mixing action tends to produce a uniform average axial velocity across the stream. The change from the laminar flow pattern to the turbulent flow pattern is gradual, with no distinct transition point. For Reynolds numbers above 10,000, flow is definitely turbulent. The coef ficients of discharge of the various head-type flowmeters changes with Reynolds number (Figure 2.15b). The value for k in the basic flow equations includes a Reynolds number factor. References 1 and 2 provide tables and graphs for Reynolds number factor. For head meters, this single factor is suf ficient to establish compensation in coefficient for changes in ratio of inertial to frictional forces and for the corresponding changes in flow velocity pro file; a gas flow with the same Reynolds number as a liquid flow has the same Reynolds number factor.
Compressible Fluid Flow Density in the basic equations is assumed to be constant upstream and downstream from the primary device. For gas or vapor flow, the differential pressure developed results in
© 2003 by Béla Lipták
Integral
=2% Target Meter (Best Case)
Orifice
102
103
Venturi Tube
Flow Nozzle Target Meter (Worst Case)
10
Re
Magnetic Flowmeter
Quadrant Edged Orifice
104
105
Pipeline Reynolds Number 106
FIG. 2.15b Discharge coefficients as a function of sensor type and Reynolds number.
a corresponding change in density between upstream and downstream pressure measurement points. For accurate calculations of gas flow, this is corrected by an expansion factor that has been empirically determined. Values are given in References 1 and 2. When practical, the full-scale differential pressure should be less than 0.04 times normal minimum static pressure (differential pressure, stated in inches of water, should be less than static pressure stated in PSIA). Under these conditions, the expansion factor is quite small.
Choice of Differential-Pressure Range The most common differential-pressure range for ori fices, venturi tubes, and flow nozzles is 0 to 100 in. of water (0 to 25 kPa) for full-scale flow. This range is high enough to minimize errors due to liquid density differences in the connecting lines to the differential-pressure sensor or in seal chambers, condensing chambers, and so on, caused by temperature differences. Most differential-pressure-responsive devices develop their maximum accuracy in or near this range, and the maximum pressure loss —3.5 PSI (24 kPa) —is not serious in most applications. (As shown in Figure 2.27f , the pressure loss in an orifice is about 65% when a β ratio of 0.75 is used.) The 100-in. range permits a 2:1 flow rate change in either direction to accommodate changes in operating conditions. Most differential-pressure sensors can be modi fied to cover the range from 25 to 400 in. of water (6.2 to 99.4 kPa) or more, either by a simple adjustment or by a relatively minor structural change. Applications in which the pressure loss up to 3.5 PSI is expensive or is not available can be handled either by selection of a lower differential-pressure range or by the use of a venturi tube or other primary element with highpressure recovery. Some high-velocity flows will develop more than 100 in. of differential pressure with the maximum acceptable ratio of primary element effective diameter to pipe diameter. For these applications, a higher differential pressure is indicated. Finally, for low-static-pressure (less than 100 PSIA)
2.15 Orifices
gas or vapor, a lower differential pressure is recommended to minimize the expansion factor.
Pulsating Flow and Flow “Noise” Short-period (1 sec and less) variation in differential pressure developed from a head-type flowmeter primary element arises from two distinct sources. First, reciprocating pumps, compressors, and the like may cause a periodic fluctuation in the rate of flow. Second, the random velocities inherent in turbulent flow cause variations in differential pressure even with a constant flow rate. Both have similar results and are often mistaken for each other. However, their characteristics and the procedures used to cope with them are distinct. Pulsating Flow The so-called pulsating flow from reciprocating pumps, compressors, and so on may signi ficantly affect the differential pressure developed by a head-type meter. For example, if the amplitude of instantaneous differentialpressure fluctuation is 24% of the average differential pressure, an error of ±1% can be expected under normal operation conditions. For the pulsation amplitudes of 24, 48, and 98% values, the corresponding errors of ±1, ±4, and ±16% can be expected. The Joint ASME-AGA Committee on Pulsation reported that the ratio between errors varies roughly as the square of the ratio between differential-pressure fluctuations. For liquid flow, there is indication that the average of the square root of the instantaneous differential pressure (essentially average of instantaneous flow signal) results in a lower error than the measurement of the average instantaneous differential pressure. However, for gas flow, extensive investigation has failed to develop any usable relationship between pulsation and deviation from coef ficient beyond the estimate 4 of maximum error. Operation at higher differential pressures is generally advantageous for pulsating flow. The only other valid approach to improve the accuracy of pulsating gas flow measurement is the location of the meter at a point where pulsation is minimized. Flow “Noise” Turbulent flow generates a complex pattern of random velocities. This results in a corresponding variation or “noise” in the differential pressure developed at the pressure connections to the primary element. The amplitude of the noise may be as much as 10% of the average differential pressure with a constant flow rate. This noise effect is a complex hydrodynamic phenomenon and is not fully understood. It is augmented by flow disturbances from valves, fittings, and so on both upstream and downstream from the flowmeter primary element and, apparently, by characteristics of the primary element itself. Tests based on average flow rate as accurately determined by static weight/time techniques (compared to accurate measurement of differential pressure including continuous, precise averaging of noise) indicate that the noise, when precisely
© 2003 by Béla Lipták
263
averaged, introduces negligible (less than 0.1%) measurement error when the average flow is substantially constant (change 5 of average flow rate is not more than 1% per second). It should be noted that average differential pressure, not average flow (average of the square root of differential pressure), is measured, because the noise is developed by the random, not the average, flow. Errors in the determination of true differential-pressure average will result in corresponding errors in flow measurement. For normal use, one form or another of “damping” in devices responsive to differential pressure is adequate. Where accuracy is a major concern, there must be no elements in the system that will develop a bias rather than a true average when subjected to the complex noise pattern of differential pressure. Differential-pressure noise can be reduced by the use of two or more pressure-sensing taps connected in parallel for both high and low differential-pressure connections. This provides major noise reduction. Only minor improvement results from additional taps. Piezometer rings formed of multiple connections are frequently used with venturi tubes but seldom with ori fices or flow nozzles.
THE ORIFICE METER The orifice meter is the most common head-type flow measuring device. An ori fice plate is inserted in the line, and the differential pressure across it is measured (Figure 2.15a). This section is concerned with the primary device (the ori fice plate, its mounting, and the differential-pressure connections). Devices for the measurement of the differential pressure are covered in Chapters 3 and 5. The orifice in general, and the conventional thin, concentric, sharp-edged orifice plate in particular, have important advantages that include being inexpensive manufacture to very close tolerances and easy to install and replace. Ori fice measurement of liquids, gases, and vapors under a wide range of conditions enjoys a high degree of con fidence based on a great deal of accurate test work. The standard orifice plate itself is a circular disk; usually stainless steel, from 0.12 to 0.5 in. (3.175 to 12.70 mm) thick, depending on size and flow velocity, with a hole (ori fice) in the middle and a tab projecting out to one side and used as a data plate (Figure 2.15c). The thickness requirement of the orifice plate is a function of line size, flowing temperature, and differential pressure across the plate. Some helpful guidelines are as follows. By Size 2 to 12 in. (50 to 304 mm), 0.13 in. (3.175 mm) thick 14 in. (355 mm) and larger, 0.25 in. (6.35 mm) thick By Temperature ≥600°F (316°C) 2 to 8 in. (50 to 203 mm), 0.13 in. (3.175 mm) thick 10 in. (254 mm) and larger, 0.25 in. (6.35 mm) thick
264
Flow Measurement
Vent Hole Location (Liquid Service)
Flow
Drain Hole Location (Vapor Service)
Pipe Internal Diameter
Bevel Where Thickness is Greater than 1/8 Inch (3.175 mm) 45° or the Orifice Diameter is Less than 1 Inch (25 mm)
1/8 Inch (3.175 mm) Maximum 1/8-1/2 Inch (3.175−12.70 mm)
FIG. 2.15c Concentric orifice plate.
Flow through the Orifice Plate The orifice plate inserted in the line causes an increase in flow velocity and a corresponding decrease in pressure. The flow pattern shows an effective decrease in cross section beyond the orifice plate, with a maximum velocity and minimum pressure at the vena contracta (Figure 2.15a). This location may be from 0.35 to 0.85 pipe diameters downstream from the orifice plate, depending on β ratio and Reynolds number. This flow pattern and the sharp leading edge of the ori fice plate (Figure 2.15d) that produces it are of major importance. The sharp edge results in an almost pure line contact between the plate and the effective flow, with negligible fluid-to-metal friction drag at this boundary. Any nicks, burrs, or rounding of the sharp edge can result in surprisingly large measurement errors. When the usual practice of measuring the differential pressure at a location close to the ori fice plate is followed, friction effects between fluid and pipe wall upstream and downstream from the orifice are minimized so that pipe roughness has minimum effect. Fluid viscosity, as re flected in Reynolds number, does have a considerable in fluence, particularly at low Reynolds numbers. Because the formation of the vena contracta is an inertial effect, a decrease in the ratio of inertial to frictional forces (decrease in Reynolds number) and the
corresponding change in the flow profile result in less constriction of flow at the vena contracta and an increase of the flow coef ficient. In general, the sharp edge ori fice plate should not be used at pipe Reynolds numbers under 2000 to 10,000 or more (Table 2.1e). The minimum recommended Reynolds number will vary from 10,000 to 15,000 for 2-in. (50-mm) through 4-in. (102-mm) pipe sizes for β ratios up to 0.5, and from 20,000 to 45,000 for higher β ratios. The Reynolds number requirement will increase with pipe size and β ratio and may range up to 200,000 for pipes 14 in. (355 mm) and 6 larger. Maximum Reynolds numbers may be 10 through 4-in. 7 (102-mm) pipe and 10 for larger sizes.
Location of Pressure Taps For liquid flow measurement, gas or vapor accumulations in the connections between the pipe and the differential-pressure measuring device must be prevented. Pressure taps are generally located in the horizontal plane of the centerline of horizontal pipe runs. The differential-pressure measuring device is either mounted close-coupled to the pressure taps or connected through downward sloping connecting pipe of suf ficient diameter to allow gas bubbles to flow up and back into the line. For gas, similar precautions to prevent accumulation of liquid are required. Taps may be installed in the top of the line, with upward sloping connections, or the differentialpressure measuring device may be close-coupled to taps in the side of the line (Figure 2.15e). For steam and similar vapors that are condensable at ambient temperatures, condensing chambers or their equivalent are generally used, usually with down-sloping connections from the side of the pipe to the measuring device. There are five common locations for the differential-pressure taps: flange taps, vena contracta taps, radius taps, full- flow or pipe taps, and corner taps. In the United States, flange taps (Figures 2.15e and 2.15f ) are predominantly used for pipe sizes 2 in. (50 mm) and larger. The manufacturer of the ori fice flange set drills the taps so
2.125" (54mm) Block Valve
Equalizing Valve
FIG. 2.15d Flow pattern with orifice plate.
© 2003 by Béla Lipták
FIG. 2.15e Measurement of gas flow with differential pressure transmitter and 3 three-valve manifold.
2.15 Orifices
265
Center of Tees Exactly at Same Level
1/2" Plug Cock
1/2" Line Pipe
FIG 2.15g Corner tap installation.
FIG 2.15f 3 Steam flow measurement using standard manifold.
that the centerlines are 1 in. (25 mm) from the ori fice plate surface. This location also facilities inspection and cleanup of burrs, weld metal, and so on that may result from installation of a particular type of flange. Flange taps are not recommended below 2 in. (50 mm) pipe size and cannot be used below 1.5 in. (37.5 mm) pipe size, since the vena contracta may be closer than 1 in. (25 mm) from the ori fice plate. Flow for a distance of several pipe diameters beyond the vena contracta tends to be unstable and is not suitable for differential-pressure measurement (Figure 2.15a). Vena contracta taps use an upstream tap located one pipe diameter upstream of the ori fice plate and a downstream tap located at the point of minimum pressure. Theoretically, this is the optimal location. However, the location of the vena contracta varies with the ori fice-to-pipe diameter ratio and is thus subject to error if the ori fice plate is changed. A tap location too far downstream in the unstable area may result in inconsistent measurement. For moderate and small pipe, the location of the vena contracta is likely to lie at the edge of or under the flange. It is not considered good piping practice to use the hub of the flange to make a pressure tap. For this reason, vena contracta taps are normally limited to pipe sizes 6 in. (152 mm) or larger, depending on the flange rating and dimensions. Radius taps are similar to vena contracta taps except that the downstream tap is located at one-half pipe diameter (one radius) from the ori fice plate. This practically assures that the tap will not be in the unstable region, regardless of ori fice diameter. Radius taps today are generally considered superior to the vena contracta tap, because they simplify the pressure
© 2003 by Béla Lipták
tap location dimensions and do not vary with changes in orifice β ratio. The same pipe size limitations apply as to the vena contracta tap. Pipe taps are located 2.5 pipe diameters upstream and 8 diameters downstream from the ori fice plate. Because of the distance from the orifice, exact location is not critical, but the effects of pipe roughness, dimensional inconsistencies, and so on are more severe. Uncertainty of measurement is perhaps 50% greater with pipe taps than with taps close to the orifice plate. These taps are normally used only where it is necessary to install an ori fice meter in an existing pipeline and radius or where vena contracta taps cannot be used. Corner taps (Figure 2.15g) are similar in many respects to flange taps, except that the pressure is measured at the “corner” between the ori fice plate and the pipe wall. Corner taps are very common for all pipe sizes in Europe, where relatively small clearances exist in all pipe sizes. The relatively small clearances of the passages constitute possible sources of trouble. Also, some tests have indicated inconsistencies with high β ratio installations, attributed to a region of flow instability at the upstream face of the ori fice. For this situation, an upstream tap one pipe diameter upstream of the orifice plate has been used. Corner taps are used in the United States primarily for pipe diameters of less than 2 in. (50 mm).
ECCENTRIC AND SEGMENTAL ORIFICE PLATES The use of eccentric and segmental ori fices is recommended where horizontal meter runs are required and the fluids contain extraneous matter to a degree that the concentric ori fice would plug up. It is preferable to use concentric ori fices in a vertical meter tube if at all possible. Flow coef ficient data is limited for these orifices, and they are likely to be less accurate. In the absence of speci fic data, concentric ori fice data may be applied as long as accuracy is of no major concern. The eccentric ori fice plate, Figure 2.15h, is like the concentric plate except for the offset hole. The segmental ori fice
266
Flow Measurement
Eccentric
45° 45°
45°
45° c i r t n e c c E
Zone for Pressure Taps For Gas Containing Liquid or For Liquid Containing Solids
For Liquid Containing Gas
FIG. 2.15h Eccentric orifice plate.
Zone for Pressure Taps
Segmental
20°
20° 45°
45°
45°
45°
20°
20°
QUADRANT EDGE AND CONICAL ENTRANCE ORIFICE PLATES
l a t n e m g e S
R
For Vapor Containing Liquid or For Liquid Containing Solids
or gasket interferes with the hole on either type plate. The equivalent β for a segmental ori fice may be expressed as β = a / A , where a is the area of the hole segment, and A is the internal pipe area. In general, the minimum line size for these plates is 4 in. (102 mm). However, the eccentric plate can be made in smaller sizes as long as the hole size does not require beveling. Maximum line sizes are unlimited and contingent only on calculation data availability. Beta ratio limits are limited to between 0.3 and 0.8. Lower Reynolds number limit is 2000D (D in inches) but not less than 10,000. For compressible fluids, ∆P/P1 ≤ 0.30, where ∆P and P1 are in the same units. Flange taps are recommended for both types of ori fices, but vena contracta taps can be used in larger pipe sizes. The taps for the eccentric ori fice should be located in the quadrants directly opposite the hole. The taps for the segmental orifice should always be in line with the maximum dam height. The straight edge of the dam may be beveled if necessary using the same criteria as for a square edge ori fice. To avoid confusion after installation, the tabs on these plates should be clearly stamped “eccentric” or “segmental.”
For Liquid Containing Gas
Pressure taps must always be located in solid area of plate and centerline of tap not nearer than 20° from intersection point of chord and arc.
FIG. 2.15i Segmental orifice plate.
plate, Figure 2.15i, has a hole that is a segment of a circle. Both types of plates may have the hole bored tangent to the inside wall of the pipe or more commonly tangent to a concentric circle with a diameter no smaller than 98% of the pipe internal diameter. The segmental plate is parallel to the pipe wall. Care must be taken so that no portion of the flange
The use of quadrant edge and conical entrance ori fice plates is limited to lower pipe Reynolds numbers where flow coefficients for sharp-edged ori fice plates are highly variable, in the range of 500 to 10,000. With these special plates, the stability of the flow coef ficient increases by a factor of 10. The minimum allowable Reynolds number is a function of β ratio, and the allowable β ratio ranges are limited. Refer to Table 2.15j for β ratio range and minimum allowable Reynolds number. The maximum allowable pipe Reynolds number ranges from 500,000 × (β – 0.1) for quadrant edge to 200,000 × (β ) for the conical entrance plate. The conical entrance also has a minimum D ≥ 0.25 in. (6.35 mm). For compressible fluids, ∆P/P1 ≤ 0.25 where ∆P and P1 are in the same units Flange pressure taps are preferred for the quadrant edge, but corner and radius taps can also be used with the same flow coef ficients. For the conical entrance units, reliable data
TABLE 2.15j Minimum Allowable Reynolds Numbers for Conical and Quadrant Edge Orifices Type
Conical entrance
Quadrant edge
© 2003 by Béla Lipták
Re Limits
β
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
Re
25
28
30
33
35
38
40
43
45
48
β
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
Re
50
53
55
58
60
63
65
68
70
73
75
β
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Re
250
300
400
500
700
1000
1700
3300
2.15 Orifices
Radius r ± 0.01 r
TABLE 2.15m Selecting the Right Orifice Plate for a Particular Application
45°
Flow
d ± 0.001 d W=1.5 d< D
FIG. 2.15k Quadrant edge orifice plate. < 0.1 D
45° ± 1°
Flow
0.084 d ± 0.003 d
Orifice Type
Appropriate Process Fluid
Reynolds Number Range
Normal Pipe Sizes, in. (mm)
Concentric, square edge
Clean gas and liquid
Over 2000
0.5 to 60 (13 to 1500)
Concentric, quadrant, or conical edge
Viscous clean liquid
200 to 10,000
1 to 6 (25 to 150)
Eccentric or segmental square edge
Dirty gas or liquid
Over 10,000
4 to 14 (100 to 350)
THE INTEGRAL ORIFICE
Equal to r
d ± 0.001 d
> 0.2d < D
Miniature flow restrictors provide a convenient primary element for the measurement of small fluid flows. They combine a plate with a small hole to restrict flow, its mounting and connections, and a differential-pressure sensor —usually a pneumatic or electronic transmitter. Units of this type are often referred to as integral orifice flowmeters. Interchangeable flow restrictors are available to cover a wide range of flows. A common minimum standard size is a 0.020-in. (0.5-mm) throat diameter, which will measure water flow down to 3 0.0013 GPM (5 cm /min) or airflow at atmospheric pressure 3 down to 0.0048 SCFH (135 cm /min) (Figure 2.15n).
0.021 d ± 0.003 d
FIG. 2.15l Conical entrance orifice plate.
is available for corner taps only. A typical quadrant edge plate is shown in Figure 2.15k, and a typical conical entrance orifice plate is shown in Figure 2.15l. These plates are thicker and heavier than the normal sharp-edge type. Because of the critical dimensions and shape, the quadrant edge is dif ficult to manufacture; it is recommended that it be purchased from skilled commercial fabricators. The conical entrance is much easier to make and could be made by any quali fied machine shop. While these special ori fice forms are very useful for lower Reynolds numbers, it is recommended that, for a pipe Re > 100,000, the standard sharp-edge ori fice be used. To avoid confusion after installation, the tabs on these plates should be clearly stamped “quadrant” or “conical.” An application summary of the different ori fice plates is given in Table 2.15m. For dirty gas service, the annular ori fice plate (Figure 2.24a) can also be considered.
© 2003 by Béla Lipták
267
Low Pressure Chamber Integral Orifice
To Low Pressure Chamber
FIG. 2.15n Typical integral orifice meter.
High Pressure Chamber
From High Pressure Chamber
268
Flow Measurement
Miniature flow restrictors are used in laboratory-scale processes and pilot plants, to measure additives to major flow streams, and for other small flow measurements. Clean fluid is required, particularly for the smaller sizes, not only to avoid plugging of the small ori fice opening but because a buildup of even a very thin layer on the surface of the element will cause an error. There is little published data on the performance of these small restrictors. These are proprietary products with performance data provided by the supplier. Where accuracy is important, direct flow calibration is recommended. Water flow calibration, using tap water, a soap watch, and a glass graduate (or a pail and scale) to measure total flow, is readily carried out in the instrument shop or laboratory. For viscous liquids, calibration with the working fluid is preferable, because viscosity has a substantial effect on most units. Calibration across the working range is recommended, given that precise conformity to the square law may not exist. Some suppliers are prepared to provide calibrated units for an added fee.
INSTALLATION The orifice is usually mounted between a pair of flanges. Care should be exercised when installing the ori fice plate to be sure that the gaskets are trimmed and installed such that they do not protrude across the face of the ori fice plate beyond the inside pipe wall (Figure 2.15o). A variety of special devices are commercially available for mounting orifice plates, including units that allow the ori fice plate to be inserted and removed from a flowline without interrupting the flow (Figure 2.15p). Such manually operated or motorized orifice fittings can also be used to change the
Operating 11 Grease Gun 23
12
9 9A 10 B Bleeder Valve
7
6 1 Equalizer Valve
5 Slide Valve To Remove Orifice Plate
To Replace Orifice Plate
(A) (B) (C) (D) (E) (F) (G) (H) (I)
Open No. 1 (Max. Two Turns Only) Open No. 5 Rotate No. 6 Rotate No. 7 Close No. 5 Close No. 1 Open No. 10 B Lubricate thru No. 23 Loosen No. 11 (do not remove No. 12) (J) Rotate No. 7 to free Nos. 9 and 9A (K) Remove Nos. 12, 9, and 9A
(A) Close 10 B (B) Rotate No. 7 Slowly Until Plate Carrier is Clear of Sealing Bar and Gasket Level. Do Not Lower Plate Carrier onto Slide Valve. (C) Replace Nos. 9A, 9, and 12 (D) Tighten No. 11 (E) Open No. 1 (F) Open No. 5 (G) Rotate No. 7 (H) Rotate No. 6 (I) Close No. 5 (J) Close No. 1 (K) Open 10 B (L) Lubricate thru No. 23 (B) Close No. 10 B
11 12 9 9A
10 B
23 7
5 6
Flow
Important: Remove Burrs After Drilling
FIG. 2.15o Prefabricated meter run with inside surface of the pipe machined for smoothness after welding for a distance of two diameters from each flange face. The mean pipe ID is averaged from four measurements 3 made at different points. They must not differ by more than 0.3%.
© 2003 by Béla Lipták
Side Sectional Elevation
FIG. 2.15p Typical orifice fitting. (Courtesy of Daniel Measurement and Control.)
2.15 Orifices
flow range by sliding a different ori fice opening into the flowing stream. To avoid errors resulting from disturbance of the flow pattern due to valves, fittings, and so forth, a straight run of smooth pipe before and after the ori fice is recommended. Required length depends on β ratio (ratio of the diameter of the orifice to inside diameter of the pipe) and the severity of the flow disturbance. For example, an upstream distance to the ori fice plate of 45 pipe diameters with 0.75 β ratio is the minimum recommendation for a throttling valve. For a single elbow at the same β , the minimum distance would be only 17 pipe diameters. Figure 2.15q gives minimum values for a variety of upstream disturbances. Upstream lengths greater than the minimum are recommended. A downstream pipe run of five pipe diameters from the ori fice plate is recommended in all cases. This straight run should not be interrupted by thermowells or other devices inserted into the pipe. Where it is not practical to install the ori fice in a straight run of the desired length, the use of a straightening vane to eliminate swirls or vortices is recommended. Straightening vanes are manufactured in various con figurations (Figure 2.15r) and are available from commercial meter tube fabricators. They should be installed so that there are at least two pipe diameters between the disturbance source and vane entry and at least six pipe diameters from the vane exit to the upstream high pressure tap of the ori fice. The installation of the pressure taps is important. Burrs and protrusions at the tap entry point must be removed. (Figure 2.15o). The tap hole should enter the line at a right angle to the inside pipe wall and should be slightly beveled. Considerable error can result from protrusions that react with the flow and generate spurious differential pressure. Careful installation is particularly important when full- flow taps are located in areas of full pipe velocity and in positions that are dif ficult to inspect.
LIMITATIONS Certain limitations exist in the application of the concentric, sharp-edged orifice. 1. The concentric orifice plate is not recommended for slurries and dirty fluids, where solids may accumulate near the orifice plate (Table 2.15m). 2. The sharp-edged orifice plate is not recommended for strongly erosive or corrosive fluids, which tend to round over the sharp edge. Ori fice plates made of materials that resist erosion or corrosion are used for conditions that are not too severe. 3. For flows at less than 10,000 Reynolds number (determined in the pipe), the correction factor for Reynolds number may introduce problems in determining the
© 2003 by Béla Lipták
269
total flow when the flow rate varies considerably (Figure 2.15b). The quadrant-edged ori fice plate is recommended for this application in preference to the sharp-edged plate (Table 2.15m). 4. For liquids with entrained gas or vapor, a “vent hole” in the plate can be used for horizontal meter runs to prevent accumulation of gas ahead of the ori fice plate (Figure 2.15c). If the diameter of the vent hole is less than 10% of the ori fice diameter, then the flow is less than 1% of the total flow. If this error cannot be tolerated, appropriate correction can be made to the ori fice calculation. On dirty service, vent or drain holes are considered to be of little value, because they are subject to plugging; they are not recommended. 5. In a similar fashion, a drain or weep hole can be provided for gas with entrained liquid. However, it is recommended that meters for liquid with entrained gas or gas with entrained liquid services be installed vertically. Normally, the flow direction would be upward for liquids and downward for gases. For severe entrainment situations, eccentric or segmental ori fice plates should be used. 6. The basic flow equations are based on flow velocities well below sonic. Ori fice measurement is also used for flows approaching sonic velocity but requires a different theoretical and computational approach. 7. For concentric ori fice plates, it is recommended that the β ratio be limited to a range of 0.2 to 0.65 for best accuracy. In exceptional cases, this can be extended to a range of 0.15 to 0.75. 8. For large flows, the pressure loss through an ori fice can result in signi ficant cost in terms of power requirements (see Section 2.1). Venturi tubes with relatively large pressure recovery substantially decrease the pressure loss. Lo-Loss Tubes, Dall Tubes, Foster Flow Tubes, and similar proprietary primary elements develop 95% or better pressure recovery. The pressure loss is less than 5% of differential pressure (see Figure 2.29f ). Elbow taps involve no added pressure loss (see Section 2.6). Pitot tube elements introduce negligible loss. Ori fice plates can be sized for full-scale differential pressure ranging from 5 in. (127 mm) of water to several hundred inches of water. Most commonly the range is from 20 to 200 in. (508 to 5080 mm) of water. The pressure recovery ratio of an orifice (except for pipe taps) can be estimated by 2 (1 − β ). 9. For compressible fluids, ∆P/P1 should be ≤0.25 where ∆P and P1 are in the same units. This will minimize the errors and corrections required for density changes in flow through the orifice. 10. The use of vent and drain holes is discouraged, if in order to keep them from plugging, they would need to be large enough to adversely affect accuracy.
270
Flow Measurement
For Orifices and Flow Nozzles
For Orifices and Flow Nozzles
Fittings in Different Planes
Fittings in Different Planes
Va ves 50
Orifice or Orifice or Flow Nozzle
Orifice or Flow Nozzle
A
B
10
Ells, Tube Turns or
Diam.
Long Radius Bends
Flow Nozzle
B A Ells, Tube Turns, or
50
A B Straightening Vane
40
C
Long Radius Bends 40
30
Orifice or Flow Nozzle
C 30
B
Vane 2 Diam. Long o Eb
A
w
Lo
T
o
A'
20
T
C
A
10
b
E
A
R
Lo
ow
20
B ng
R
A'
e i p P t h i g a t r S r t e e m i a D
S a nd
obe A G A Ga
20
ao
e
e Va v
op
W
de
O
p 10
es Va v
C Fo A
0
C
0 70 80 90
10 20 30 40 50 60 D ame e Ra o Fo Ven u Tubes
0
70 80 90
10 20
30
40
0 70 80 90
50 60
Based on Da a F om W S Pa doe
D ame e Ra o
Ven u
For Orifices and Flow Nozzles
For Orifices and Flow Nozzles
all Fittings in Same Plane
all Fittings in Same Plane
A
Ven u
Orifice or Flow Nozzle
Orifice or Flow Nozzle
D
e A R
u
B 0
10 20 30 40 50 60 D ame e Ra o
10
c
B
0
g
30
2 Diam. S a gh en ng
A
ng
R
B
Vane 2 D am Long
A
B
A'
Orifice or Flow Nozzle
C A' 2 Diam. Straightening
40
B
A
A'
B
A
B
A'
B
LRBs
Ells, Tube Turns, or LRBs
A
D A
B
A
B
A B
B
12 D am
Straightening Ven u C
A D um o Tank
C
B
B
30
Long A
A
Flow Nozzle 20
20 Orifice or
Sepa a o
Flow Nozzle
A' A
B
B
C
A
10
E
w
bo
B
0
10 20
30
40
50 60
A
A' C
10
B
0 70 80 90
0
D ame e Ra o
10 20 30 40 50 60 D ame e Ra o
10
30
2 Diam. Orifice or
Bends
D = 6 D am
B
B
A' Rad us
2 Diam. A
A e i p P t h i g a t r S r t e e m i a D
B
0
Fo O
0 50 Ra o 1 2 3 4 5 6
Tees 45 E s Ga e va ves Sepa a o s Y F ngs Expans on JTS
50 60 Ra o 1 2 3 4 5
Tees Expans on JTS Ga e Va ves Y F ngs Sepa a o n e Neck s One D am Lg
ces and F ow Nozz es
w h Reduce s and Expande s Orifice or Flow Nozzle
0 70 80 90 C
60 70 Ra o
70 80 Ra o
1 Ga e Va ves 2 Y F ngs 3 Sepa a o n e Neck s One D am Long
1 Ga e Va ve 2 Long Rad us Bend
As Requ ed
B
B
A
Straightening Vanes
20
by P eced ng F
ngs A
C
10
B
0 0
10 20
30
40
50 60
D ame e Ra o
FIG. 2.15q Orifice straight-run requirements. (Reprinted courtesy of The American Society of Mechanical Engineers.)
© 2003 by Bé a L p ák
e i p P t h i g a t r S r t e e m i a D
0 70 80 90
10 20 30 40 50 60 Diameter Ratio
A
F ngs A owed on Ou e S de n P ace o S a gh P pe
20
40
Vane 2 Diam. Long
A Straightening Vane
D
B
70 80 90
m i a D
2.15 Orifices
271
The Old Approach Before the proliferation of computers, approximate calculations were used, giving only moderate accuracy. These are illustrated below more for historical perspective than as a recommended technique. Figure 2.15s illustrates how ori fice bore diameters were approximated, and Table 2.15t lists the maximum air, water, and steam flow capacities for both flange and pipe tap installations at various pressure drops. When using Figure 2.15s, the following equations were used to determine the orifice bore. For liquid flow,
FIG 2.15r Straightening vane.
ORIFICE BORE CALCULATIONS Z =
Accurate flow calibration, traceable to recognized standards and using the working fluid under service conditions, is difficult and expensive. For large gas flows, it is nearly impossible and is rarely done. A major advantage of ori fice metering is the ease with which flow can be accurately determined from a few simple, readily available measurements. In particular, for the concentric, sharp-edged ori fice, measurement confidence is supported by a large body of experience and precise, painstaking tests. Precise flow calculations are quite complex, although the calculation methods and equations have been well standardized. These calculation methods are thoroughly covered in the references at the end of this section. Most, if not all, of the calculations have been automated using readily available computer software for both volumetric and mass flow calculations.
5.663 ER hG f
2.15(5)
GPM Gt
For steam,* 358.9 ERY h lbm / hr V
2.15(6)
7727 ERY hP f SCFH GT f
2.15(7)
Z =
For gas,* Z =
* For steam and gas, h expressed in inches H2O should be equal to or less than P f expressed in PSIA units.
Pipe Constants Pipe I. D.
A-2 1.000
.110 A-1 1.00
.100
.90
.090
Curve A-2 Curve A-1
.80
.70 z r o t c .60 a F w o l F .50
.080
Curve B
Y .980 r .960 o t c a F .940 y t i l .920 i b i s .900 s e r p .880 m o C .860
d D .10 .40 .50 .60 .70 .75 .80
.840
.070
0
1
2 3 4 5 6 7 Pressure Loss Ratio - x
8
9 10
.060
.040
.30
.030
.20
.020
.10
.010 .100
.957 1.049 1.380 1.500 1.610 1.939 2.067 2.323 2.469 2.900 3.068 3.826 4.026
.00543 .00653 .01130 .01334 .01537 .02230 .02534 .03200 .03614 .04987 .0558 .0868 .0961
6.625 7.023 7.625 7.981 8.071 9.750 10.020 10.136 11.750 11.938 12.000 12.090 13.250
4.063 4.813 5.047 5.761 6.065
.0979 .1374 .1511 .1968 .2181
14.250 15.250 17.182 19.182
E1.020 r o1.010 t c a F1.000 a e r .990 A -200
.150
.200
.250
.300
.350
.400
.450
.500
.550
.600
18 - 8 Ever-Dur
Curve C
Monel
Steel
0 200 400 600 Flowing Temperature - °F.
.650
.700
.750
Orifice Ratio - d D
FIG. 2.15s Orifice bore determination chart (flange taps). © 1946 by Taylor Instrument Companies. (ABB Kent-Taylor Inc.)
© 2003 by Béla Lipták
Pipe I. D.
Pipe Constant
Pipe Constant (R) = 0.00593 (I. D.)2
.050
.40
Pipe Constant
800
.800
.2603 .2925 .3448 .3777 .3863 .5637 .5954 .6092 .8187 .8451 .8539 .8668 1.0411 1.2042 1.3791 1.7507 2.1819
272
Flow Measurement
TABLE 2.15t Orifice Flowmeter Capacity Table* Flange and Vena Contracta Taps Liquid
Steam
Gas
Pipe Taps Liquid
Steam
Gas
Pipe Size
Actual Inside Diam. (I.D.) Sched. 40
Maximum Orifice Diam.
Meter Range
Water (SG = 1)
100 PSIG Saturated
Air (SG = 1.0) @ 100 PSIG and 60°F
Water (SG = 1)
100 PSIG Saturated
Air (SG = 1.0) @ 100 PSIG and 60°F
Inches
Inches
Inches
Inches of Water
Gal./Min.
Lb./Hr.
Std. Cu. Ft/Min.
Gal./Min.
Lb./Hr.
Std. Cu. Ft./Min.
200 100 50 20 10 2.5
10.6 7.5 5.3 3.3 2.4 1.17
338 239 170 107 76 38
119 84 59 37 27 13
15.7 11.2 7.9 5.0 3.5 1.7
506 358 253 160 113 56
178 126 89 57 40 20
200 100
30 21.2
963 682
295 239
44.8 31.7
1440 1017
507 358
50 20 10 2.5
15.0 9.5 6.7 3.35
482 305 216 108
170 108 76 38
22.4 14.2 10.1 5.0
719 455 323 161
253 160 113 56
1.127
200 100 50 20 10 2.5
70.7 50.1 35.1 22.4 15.8 7.9
2270 1600 1135 718 683 254
796 564 399 253 178 90
105 75 52.7 33.4 23.6 11.8
3380 2390 1690 1070 758 379
1190 844 596 378 267 133
1.448
200 100 50 20 10 2.5
116 83 58.5 37.0 26.1 13.1
3740 2645 1870 1183 840 420
1313 932 658 417 295 148
174 123 87 55 39 19.4
5580 3950 2790 1768 1252 625
1966 1390 983 623 440 220
2.147
200 100 50 20 10 2.5
255 181 128 81.5 57.5 28.8
8240 5830 4125 2610 1843 915
2905 2080 1460 922 653 325
383 271 191 121 86 43
12300 8700 6160 3900 2760 1366
4330 3070 2175 1375 975 485
3.02
200 100 50 20 10 2.5
512 362 255 162 115 57
16400 11600 8170 5180 3670 1820
5780 4090 2890 1830 1290 647
764 540 382 242 172 85
24500 17300 12200 7730 5470 2710
8630 6100 4310 2730 1930 965
200 100 50
800 557 402
25600 18200 12900
9050 6410 4530
1190 845 598
38200 27100 19200
13500 9560 6760
253 180 90
8110 5750 2880
2870 2020 1010
378 268 134
12100 8580 4290
4280 3020 1510
1 2
1
1 12
2
3
4
5
© 2003 by Béla Lipták
0.622
1.049
1.610
2.067
3.068
4.026
5.047
0.435
0.734
3.78
20 10 2.5
2.15 Orifices
273
TABLE 2.15t Continued Orifice Flowmeter Capacity Table* Flange and Vena Contracta Taps Liquid
Steam
Gas
Pipe Taps Liquid
Steam
Gas
Pipe Size
Actual Inside Diam. (I.D.) Sched. 40
Maximum Orifice Diam.
Meter Range
Water (SG = 1)
100 PSIG Saturated
Air (SG = 1.0) @ 100 PSIG and 60°F
Water (SG = 1)
100 PSIG Saturated
Air (SG = 1.0) @ 100 PSIG and 60°F
Inches
Inches
Inches
Inches of Water
Gal./Min.
Lb./Hr.
Std. Cu. Ft/Min.
Gal./Min.
Lb./Hr.
Std. Cu. Ft./Min.
6
6.065
8
10
12
14
16
18
7.981
10.020
12.000
13.126
15.000
16.876
© 2003 by Béla Lipták
200 100 50 20 10 2.5
1158 820 580 367 258 129
37100 26300 18600 11700 8310 4150
13100 9250 6540 4140 2930 1460
1730 1223 866 547 387 193
55300 39200 27700 17500 12400 6200
19500 13800 9760 6180 4370 2180
200 100
2000 1413
64104 45320
22511 15952
2980 2110
95709 67682
33692 23853
50 20 10 2.5
1000 634 447 223
32052 20275 14386 7186
11285 7156 5054 2534
1492 943 668 333
47855 30263 21468 10719
16846 10674 7543 3772
7.5150
200 100 50 20 10 2.5
3150 2230 1578 998 706 352
101020 71481 50510 31950 22671 11324
35475 25138 17785 11277 7964 3994
4700 3325 2355 1487 1052 525
150825 106658 75413 47691 33830 16891
53094 37589 26547 16821 11887 5944
9.0000
200 100 50 20 10 2.5
4520 3200 2270 1430 1012 507
145000 103000 72400 46000 32400 16200
51300 36200 25600 16200 11500 5740
6750 4775 3380 2135 1512 757
216000 153000 108000 68600 48300 24200
76500 45100 38200 24200 17100 8560
9.8445
200 100 50 20 10 2.5
5415 3830 2710 1715 1210 603
173398 122588 86699 54842 38914 19437
60891 43148 30526 19356 13670 6855
8060 5720 4040 2555 1808 900
258887 183076 129443 81860 58068 28994
91135 64520 45567 28873 20404 10202
11.2500
200 100 50 20 10 2.5
7065 5000 3535 2240 1580 788
226442 160089 113221 71619 50818 25383
79518 56347 39864 25277 17852 8952
10520 7460 5275 3335 2360 1175
338084 239081 169042 106902 75832 37865
119014 84258 59507 37705 26646 13323
200 100 50
8920 6330 4475
286324 202424 143162
100546 71248 50406
13320 9270 6675
427489 302305 213744
150487 106539 75243
2830 1995 995
90558 64256 32095
31962 22573 11320
4220 2985 1485
135172 95885 47876
47676 33693 16847
4.55
5.9858
12.6570
20 10 2.5
274
Flow Measurement
TABLE 2.15t Continued Orifice Flowmeter Capacity Table* Flange and Vena Contracta Taps Liquid
Steam
Gas
Pipe Taps Liquid
Steam
Gas
Pipe Size
Actual Inside Diam. (I.D.) Sched. 40
Maximum Orifice Diam.
Meter Range
Water (SG = 1)
100 PSIG Saturated
Air (SG = 1.0) @ 100 PSIG and 60°F
Water (SG = 1)
100 PSIG Saturated
Air (SG = 1.0) @ 100 PSIG and 60°F
Inches
Inches
Inches
Inches of Water
Gal./Min.
Lb./Hr.
Std. Cu. Ft/Min.
Gal./Min.
Lb./Hr.
Std. Cu. Ft./Min.
20
18.814
24
14.1105
22.626
200 100 50 20 10 2.5
11100 7870 5565 3520 2485 1240
356238 251352 178119 112671 79946 39932
125097 88645 62714 39766 28085 14084
16550 11720 8310 5250 3715 1850
531871 376121 265936 168177 119298 59566
187232 132554 93616 59318 41920 20960
200 100
16060 11375
515222 364250
180927 128206
23950 16960
769238 543978
270791 191710
8035 5090 3590 1795
257611 162954 115625 57753
90703 57513 40619 20369
12000 7585 5375 2675
384619 243233 172539 86150
135395 85790 60628 30314
50 20 10 2.5
16.9695
*
Reproduced by permission of Taylor Instrument Co. (ABB Kent-Taylor).
where E = area factor, determined from curve C on Figure 2.15s R = pipe constant, determined from table on Figure 2.15s G = specific gravity of gas (air = 1.0) G f = specific gravity of liquid at operating temperature Gt = specific gravity of liquid at 60 °F (15.6°C) h = pressure differential across ori fice in inches H 2O Y = compressibility factor, determined from curve B in Figure 2.15s 3 V = specific volume (ft /lbm), determined from steam tables provided in the Appendix T f = flowing temperature expressed in °R ( °F +460) P f = flowing pressure in PSIA X = pressure loss ratio de fined as h/2P f A useful simplified form of the mass flow equation [Equation 2.15(3)] is W
=
359 Cd 2
hρ
1 − β 4
2.15(8)
where W = mass flow in lb/h d = ori fice diameter in inches h = differential pressure in inches of water; water density 3 assumed to be 62.32 lb/ft , corresponding to 68°F (20°C) 3 ρ = operating density in lb/ft β = ratio of ori fice diameter to pipe diameter in pure number C = coef ficient of discharge in pure number
© 2003 by Béla Lipták
This is a modification of the basic equation for mass 2 flow [Equation 2.15(3)] substituting the 359 Cd 1 − β 4 for kA. The constant 359 includes a factor for the chosen units of measurement. The coef ficient of discharge is involved with the flow pattern established by the ori fice, including the vena contracta and its relation to the differential-pressure measurement taps. An average value of C = 0.607 can be used for flange and other close-up taps, which gives working equation
W
=
218d 2
hρ
1 – β 4
2.15(9)
For full flow taps, C = 0.715, and the equation becomes
W
=
275d 2
hρ
1 – β 4
2.15(10)
These working equations can be used for approximate calculations of the flow of liquids, vapors, and gases through any type of sharp-edged ori fice. When using orifices for measurement in weight units, errors in determination of ρ must be considered. (Refer to Chapter 6 for density measurement and sensors.) Accurate determination of density under flowing conditions is dif ficult, particularly for gases and vapors. In some cases, even liquids are sub ject to density changes with both temperature and pressure (for example, pure water in high-pressure boiler feedwater measurement).
2.15 Orifices
For W , d , h, and ρ given in dimensions other than those stated, simple conversion factors apply. Transfer of ρ in Equations 2.15(8) through 2.15(10) from the numerator to denominator will give volume flow in actual cubic feet per hour at flowing conditions [see Equations 2.15(2) and 2.15(3)]. Beta ratio, and hence ori fice diameter, can be calculated from a transposed form of the mass flow Equation 2.15(8).
ORIFICE ACCURACY If the purpose of flow measurement is not absolute accuracy but only repeatable performance, then the accuracy in calculating the bore diameter is not critical, and approximate calculations will suf fice. On the other hand, if the measurement is going to be the basis for the sale of, for example, valuable fluids or of large quantities of natural gas transported in high-pressure gas lines, absolute accuracy is essential, and precision in the bore calculations is critical. Some engineers believe that, instead of individually siz6 ing each orifice plate, bore diameters should be standardized. This approach would make it practical to keep spare ori fices on hand in all standard sizes. This approach seems reasonable, because the introduction of the microprocessor-based DCS systems means it is no longer important to have round figures for the full-scale flow ranges. If this approach to orifice sizing were adopted, the ori fice bore diameters and d/p cell ranges would be standardized, round values, and the corresponding maximum flow would be an uneven number that corresponds to them. If orifice bore diameters are selected from standardized sizes, the actual bore diameter required can be calculated, as is normally done, and the next size from the standard sizes (available in 0.125-in. diameter increments) can be selected. The use of this approach is practical and, although it results in an “oddball” full flow value, that is no problem for our computing equipment. In the past, to increase flow rangeability, the natural gas pipeline transport stations used a number of parallel runs (Figure 2.15u). In these systems, the flow rangeability of the
individual orifices was minimized by opening up another parallel path if the flow exceeded about 90% of full-scale flow (of the active paths) or by closing down a path when the flow in the active paths dropped to a selected low limit, such as 80%. By so limiting the rangeability, metering accuracy was kept high, but at the substantial investment of adding piping, metering hardware, and logic controls for the opening and closing of runs. Another, less expensive, choice was to use two (or more) transmitters, one for high (10 to 100%) pressure drop and the other for low (1 to 10%), and to switch their outputs depending on the actual flow. This doubled the transmitter hardware cost and added some logic expense at the receiver, but it increased the rangeability of ori fice flowmeters to about 10:1. As smart d/p transmitters with 0.1% of span error became available, another relatively inexpensive option became obtainable: the dual-span transmitter. Some smart d/p transmitters are currently available with 0.1% of span accuracy, and their spans can be automatically switched by 7 the DCS system, based on the value of measurement. Therefore, a 100:1 pressure differential range (10:1 flow range) can be obtained by automatically switching between a high (10 to 100%) and a low (1 to 10%) pressure differential span. As the transmitter accuracy at both the high and low flow condition is 0.1% of the actual span , the overall result can be a 1% of actual flow accuracy over a 10:1 flow range. Where the ultimate in accuracy is required, actual flow calibration of the meter run (the ori fice, assembled with the upstream and downstream pipe, including straightening vanes, if any) is recommended. Facilities are available for very accurate weighed water calibrations, in lines up to 24 in. (61 cm) diameter and larger, and with a wide range of Reynolds numbers. For orifice meters, highly reliable data exists for accurate transfer of coef ficient values for liquid, vapor, and gas measurement.
References 1. 2.
Run No. 1 Run No. 2 Run No. 3
3. 4. 5.
Run No. 4
FIG. 2.15u Metering accuracy can be maximized by keeping the flow through 8 the active runs between 80% and 90% of full scale.
© 2003 by Béla Lipták
275
6. 7.
Miller, R. W., Flow Measurement Handbook , 3rd ed., McGraw-Hill, New York, 1996. ASME, Fluid Meters, Their Theory and Application, Report of ASME Research Committee on Fluid Meters, American Society of Mechanical Engineers, New York. Shell Flow Meter Engineering Handbook, Royal Dutch/Shell Group, Delft, The Netherlands, Waltman Publishing Co., 1968. American Gas Association, AGA Gas Measurement Manual, American Gas Association, New York. Miller, O. W. and Kneisel, O., Experimental Study of the Effects of Orifice Plate Eccentricity on Flow Coef ficients, ASME Paper Number 68-WA/FM-1, 10, Conclusions 3, 4, 5, American Society of Mechanical Engineers, New York. Ahmad, F., A case for standardizing orifice bore diameters, InTech, January 1987. Rudbäck, S., Optimization of orifice plates, venturies and nozzles, Meas. Control, June 1991.
276
8. 9. 10. 11. 12.
13. 14.
15.
Flow Measurement
Lipták, B. G., Applying gas flow computers, Chem. Eng., December 1970. Measurement of Fluid Flow in Pipes, Using Orifice, Nozzle, and Venturi, ASME MFC-3M, December 1983. Measurement of Fluid Flow by Means of Pressure Differential Devices, ISO 5167, 1991, Amendment in 1998. Flow Measurement Practical Guide Series, 2nd ed., D. W. Spitzer, Ed., ISA, Research Triangle Park, NC. API, Orifice Metering of Natural Gas,American Gas Associat ion, Report No. 3, American Petroleum Institute, API 14.3, Gas Processors Association GPA 8185–90. Reader-Harris, M. J. and Saterry, J. A., The orifice discharge coef ficient equation, Flow Meas. Instrum., 1, January 1990. Reader-Harris, M. J., Saterry, J. A. and Spearman, E. P., The orifice plate discharge coef ficient equation—further work, Flow Meas. Instrum., 6(2), Elsevier Science, 1995. Reader-Harris, M. J. and Saterry, J. A., The Orifice Plate Discharge Equation for ISO 5167–1, Paper 24 of North Sea Flow Measurement Workshop, 1996.
Bibliography AGA/ASME, The flow of water through orifices, Ohio State University, Student Eng. Ser. Bull. 89, IV(3).
© 2003 by Béla Lipták
Ahmad, F., A case for st andardizing orifice bore diameters, InTech, January 1987. American Gas Association, Report No. 3, Orifice Metering of Natural Gas, 1985. ANSI/API 2530, Orifice metering of natural gas, ANSI , New York, 1978. ANSI/ASME MFC, Differential Producers Used for the Measurement of Fluid Flow in Pipes (Orifice, Nozzle, Venturi), ANSI, New York, December 1983. ASME, The ASME-OSI Orifice Equation, Mech. Eng., 103(7), 1981. BBI Standard 1042, Methods for the Measurement of Fluid Flow in Pipes, Orifice Plates, Nozzles and Venturi Tubes, British Standard Institution, London, 1964. Differential pressure flowmeters, Meas. Control, September 1991. Kendall, K., Orifice Flow, Instrum. Control Syst., December 1964. Sauer, H. J., Metering pulsating flow in orifice installations, InTech, March 1969. Shichman, D., Tap location for segmental orifices, Instrum. Control Syst., April 1962. Starrett, P. S., Nottage, H. B. and Halfpenny, P. F., Survey of Information Concerning the Effects of Nonstandard Approach Conditions upon Orifice and Venturi Meters, presented at the annual meeting of the ASME, Chicago, November 7–11, 1965. Stichweh, L., Gas purged DP transmitters, InTech, November 1992. Stoll, H. W., Determination of Orifice Throat Diameters, Taylor Technical Data Sheets TDS-4H603.
